When: 
Tuesday, September 23, 2014 - 4:10pm - 6:00pm
Where: 
Pardee 201
Presenter: 
Nancy Ann Neudauer, Pacific University
Price: 
Free and there will be refreshments!

In 1933, three Harvard junior-fellows tied together some
recurring themes in mathematics, into what Gian Carlo
Rota called one of the most important ideas of our day.
They were finding independence everywhere they
looked.  Do you?  We find that matroids are everywhere:  
Vector spaces are matroids;  We can define matroids on a graph.
Matroids are useful in situations that are modelled
by both graphs and matrices.  We consider how we can ask
research questions about matroids, and look into
results from a student's investigation.

Two matroids are commonly defined on a graph:  the familiar cycle matroid and the 
more rarely-encountered bicircular matroid.  
The bases of the cycle matroid are the spanning trees of the associated graph; 
the bases of the bicircular matroid are all subgraphs of the graph where each
connected component contains exactly one cycle and (possibly) other edges.
We enumerate the bases of the bicircular matroid for several classes of graphs.
For a given graph, usually there are more bases of the bicircular matroid than
the cycle matroid.  We ask when the reverse is true, and what this translates
to in terms of the structure of the graph.

No prior knowledge of matroids or graphs is needed.

 

 

Sponsored by: 
Department of Mathematics

Contact information

Name: 
c. jayne trent
Phone: 
610-330-5267
Email: 
trentj@lafayette.edu